[R-sig-ME] Odd ANOVA degrees of freedom with ZI component of glmmTMB model

[Ben Bolker]

      The difference in 'Df' between the two components, which appear to 
have the same fixed-effect model specification, is definitely surprising.

      It's not surprising that chisq=9.46 with 2 df could have a lower 
p-value than chisq=9.89 with 3 df; the larger the df (i.e. the larger 
the difference in the number of parameters/complexity between the two 
models implicitly being compared), the more dispersed the null 
distribution of the deviance difference (=='chisq').

    To troubleshoot I would look at the guts of glmmTMB:::Anova.glmmTMB 
and see what's going on. I'm not claiming that will be obvious: if you 
can post a *reproducible* example to the glmmTMB issues list I'd be 
happy to take a look.

On 2023-01-11 12:14 PM, Elliot Johnston wrote:
> Hi all,
>
> I am using the car package to run ANOVAs (type II Wald chi square tests) on
> the following model:
>
> m1 <- glmmTMB(Count ~ Time_Period*Assignment + (1|Region/Site_ID),
>                    ziformula = ~ Time_Period*Assignment + (1|Region/Site_ID),
>                    data = allbirds, family = poisson)
>
> Time Period has three levels and Assignment has two levels. When running
> the ANOVA on the conditional component -- car::Anova(m1, component =
> "cond") -- the degrees of freedom in the output is as I would expected
> (n-1):
>
>                                  Chisq    Df  Pr(>Chisq)
> Time_Period            0.9105  2    0.63429
> Assignment             2.1043  1    0.14689
> Time_Period:Assignment 6.8486  2    0.03257 *
>
> But when I run the ANOVA for the zero-inflated component -- car::Anova(m1,
> component = "zi") -- the output looks strange:
>
>                                  Chisq    Df Pr(>Chisq)
> Time_Period            9.8876  3   0.019546 *
> Assignment             9.4648  2   0.008805 **
> Time_Period:Assignment 7.9605  2   0.018681 *
>
> Why would the degrees of freedom change? FWIW this df discrepancy between
> the conditional and ZI ANOVAs does *not* happen when running the above
> glmmTMB model with subsetted data frames based on different bird guilds. It
> also seems strange that between the Time Period and Assignment terms the
> smaller chi square value leads to greater statistical significance. Do you
> agree that something seems wrong here or am I misunderstanding what is
> going on under the hood? Any ideas on how to troubleshoot?
>
> Thank you!
>
> -Elliot
>
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